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LinearAlgebra[Generic]

 NullSpace
 compute the nullspace of a Matrix

 Calling Sequence NullSpace[F](A)

Parameters

 F - the domain of computation, a field A - rectangular Matrix over values in F

Description

 • NullSpace(A) returns a basis for the linear system A x = 0 over the field F as a set of Vectors B = {b1, b2, ...}.
 • The (indexed) parameter F, which specifies the domain of computation, a field, must be a Maple table/module which has the following values/exports:
 F[0]: a constant for the zero of the ring F
 F[1]: a constant for the (multiplicative) identity of F
 F[+]: a procedure for adding elements of F (nary)
 F[-]: a procedure for negating and subtracting elements of F (unary and binary)
 F[*]: a procedure for multiplying two elements of F (commutative)
 F[/]: a procedure for dividing two elements of F
 F[=]: a boolean procedure for testing if two elements in F are equal

Examples

 > $\mathrm{with}\left(\mathrm{LinearAlgebra}[\mathrm{Generic}]\right):$
 > ${Q}_{\mathrm{0}},{Q}_{\mathrm{1}},{Q}_{\mathrm{+}},{Q}_{\mathrm{-}},{Q}_{\mathrm{*}},{Q}_{\mathrm{/}},{Q}_{\mathrm{=}}≔0,1,\mathrm{+},\mathrm{-},\mathrm{*},\mathrm{/},\mathrm{=}$
 ${{Q}}_{{0}}{,}{{Q}}_{{1}}{,}{{Q}}_{{\mathrm{+}}}{,}{{Q}}_{{\mathrm{-}}}{,}{{Q}}_{{\mathrm{*}}}{,}{{Q}}_{{\mathrm{/}}}{,}{{Q}}_{{\mathrm{=}}}{:=}{0}{,}{1}{,}{\mathrm{+}}{,}{\mathrm{-}}{,}{\mathrm{*}}{,}{\mathrm{/}}{,}{\mathrm{=}}$ (1)
 > $A≔\mathrm{Matrix}\left(\left[\left[1,2,3\right],\left[1,3,5\right],\left[0,1,2\right]\right]\right)$
 ${A}{:=}\left[\begin{array}{rrr}{1}& {2}& {3}\\ {1}& {3}& {5}\\ {0}& {1}& {2}\end{array}\right]$ (2)
 > $\mathrm{NullSpace}[Q]\left(A\right)$
 $\left\{\left[\begin{array}{r}{1}\\ {-}{2}\\ {1}\end{array}\right]\right\}$ (3)
 > $A≔\mathrm{Matrix}\left(\left[\left[1,2,3\right],\left[2,4,6\right],\left[-1,-2,-3\right]\right]\right)$
 ${A}{:=}\left[\begin{array}{rrr}{1}& {2}& {3}\\ {2}& {4}& {6}\\ {-}{1}& {-}{2}& {-}{3}\end{array}\right]$ (4)
 > $\mathrm{NullSpace}[Q]\left(A\right)$
 $\left\{\left[\begin{array}{r}{-}{2}\\ {1}\\ {0}\end{array}\right]{,}\left[\begin{array}{r}{-}{3}\\ {0}\\ {1}\end{array}\right]\right\}$ (5)